Stability analysis for power systems with price-based demand response via cobweb plot

Price-based demand response (DR) is a mechanism for dynamically managing electric energy consumption in response to varying electricity prices. Price-sensitive DR would encourage consumers to reduce energy consumption when prices are higher, thereby reducing the peak electricity demand and alleviating pressure to power systems. However, it brings additional dynamics and challenges to the real-time supply and demand balance. Specifically, price-sensitive DR loads are constantly changing based on dynamic real-time prices, and changes in DR loads will in turn impact electricity prices. This paper adopts a closed loop model between economic dispatch (ED) and the price-sensitive DR load adjustment for exploring the stability of power systems. The stability refers to the ability that the system will finally converge to a fixed point after finite iterations between the ED and the price-sensitive DR load adjustment procedure. Ellipse and exponential curves are used to represent the non-linear price elasticity characteristics of DR, and the cobweb plot is applied to analyze the stability of power systems. Numerical case studies illustrate how non-linear price elasticity DR curve parameters will affect the system stability.